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Highlights: [•] Multi-modal optimal seismic design methodology using MTMDs in 3D irregular buildings is presented. [•] The methodology enables achieving a performance-based-design. [•] The gradients required are efficiently derived analytically using the adjoint analytical method. [•] MTMDs overcome some of the limitations of single TMDs in seismic control. [•] MTMDs can mitigate both structural and nonstructural earthquake damage. [ABSTRACT FROM AUTHOR]

This paper deals with the allocation and sizing of multiple-tuned mass dampers (MTMDs) in an attempt to retrofit footbridges with multiple critical modes resulting from the excitation of pedestrian traffic. The simple and practical methodology proposed herein includes the use of an iterative analysis/redesign type procedure that converges to a given allowable level of accelerations. An example that uses this methodology to retrofit an existing footbridge is presented. [ABSTRACT FROM AUTHOR]